Sediment transport modelling : Relaxation schemes for Saint-Venant – Exner and three layer models

Emmanuel Audusse; Christophe Berthon; Christophe Chalons; Olivier Delestre; Nicole Goutal; Magali Jodeau; Jacques Sainte-Marie; Jan Giesselmann; Georges Sadaka

doi:10.1051/proc/201238005

Geodesic

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Sediment transport modelling : Relaxation schemes for Saint-Venant – Exner and three layer models

Emmanuel Audusse ¹ ; Christophe Berthon ² ; Christophe Chalons ³ ; Olivier Delestre ⁴ ; Nicole Goutal ⁵ ; Magali Jodeau ⁶ ; Jacques Sainte-Marie ⁷ ; Jan Giesselmann ⁸ ; Georges Sadaka ⁹

¹ BANG Project, INRIA-Paris-Rocquencourt & LAGA, University Paris 13 Nord, France
² Lab. J. Leray, University of Nantes, France
³ LJLL, University Paris Diderot, France
⁴ Lab. J.A. Dieudonné & EPU Sofia Nice, University of Nice, France
⁵ EDF R&D & Saint-Venant Lab., France
⁶ EDF R&D, France
⁷ BANG Project, INRIA-Paris-Rocquencourt & CETMEF, France
⁸ IAANS, University of Stuttgart, Germany
⁹ LAMFA, University of Picardie, France

ESAIM. Proceedings, Tome 38 (2012), pp. 78-98.

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Résumé

In this note we are interested in the modelling of sediment transport phenomena. We mostly focus on bedload transport and we do not consider suspension sediment processes. We first propose a numerical scheme for the classical Saint-Venant – Exner model. It is based on a relaxation approach for the whole system and it works with all sediment flux function. The stability of the scheme is investigated and some numerical tests are proposed. We exhibit that this coupled approach is more stable than the splitting approach that is mostly used in industrial softwares. Then we derive an original three layers model in order to overcome the difficulties that are encountered when using the classical Exner approach and we present a related relaxation model.

DOI : 10.1051/proc/201238005

Affiliations des auteurs :

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     author = {Emmanuel Audusse and Christophe Berthon and Christophe Chalons and Olivier Delestre and Nicole Goutal and Magali Jodeau and Jacques Sainte-Marie and Jan Giesselmann and Georges Sadaka},
     title = {Sediment transport modelling : {Relaxation} schemes for {Saint-Venant} {\textendash} {Exner} and three layer models},
     journal = {ESAIM. Proceedings},
     pages = {78--98},
     publisher = {mathdoc},
     volume = {38},
     year = {2012},
     doi = {10.1051/proc/201238005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201238005/}
}

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Emmanuel Audusse; Christophe Berthon; Christophe Chalons; Olivier Delestre; Nicole Goutal; Magali Jodeau; Jacques Sainte-Marie; Jan Giesselmann; Georges Sadaka. Sediment transport modelling : Relaxation schemes for Saint-Venant – Exner and three layer models. ESAIM. Proceedings, Tome 38 (2012), pp. 78-98. doi : 10.1051/proc/201238005. http://geodesic.mathdoc.fr/articles/10.1051/proc/201238005/

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